Friction Stir Welding (FSW) process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the Arbitrary Lagrangian Eulerian (ALE) formulation, remeshing or the Orthogonal Sub-Grid Scale method (OSS). It is shown that these two formulations essentially deliver the same results.